In this talk I will review some of the recent developments in the S-matrix Bootstrap focussing on applications to effective field theories. As an example, I will apply the bootstrap methods to the supergravity effective field theory in ten dimensions. I will show the improved numerical bootstrap bounds on the first correction to the universal graviton scattering and compare the result with the String Theory predictions. In the last part, I will comment on some new numerical ideas that will boost the explorations in different dimensions and for higher dimensional operators.